Internal Statistcs of a Single Natural Image

The Weizmann Institute of Science
Faculty of Mathematics and Computer Science
Computer Vision Lab

Internal vs. External SR
Statistical priors are often used to constrain ill-posed problems in Computer Vision. The quality of a prior is determined by how well it predicts the ‘correct’ solution among the infinitely many possible solutions of the under-determined problem. Next we compare the “predictive power” of the internal statistics vs. external statistics in the case of ill-posed problem of Super-Resolution (image upsampling). We use the prediction method of “Example-based Super-Resolution” (W. T. Freeman, T. R. Jones and E. C. Pasztor, Example-Based Super-Resolution, Computer Graphics and Applications,2002,22(2)). Please see the Section 4 in the paper for more details.
Below prediction error and the prediction uncertainty (Fig. 7 in Section 4) are presented to compare “predictive power” of internal vs. external statistics in case of Example-based Super-Resolution.

Prediction Error

Prediction Uncertainty

The prediction uncertainty is much higher externally than internally (for any database size), alluding to the fact that general external statistics is more prone to ‘hallucinations’ and bluriness than internal image-specific statistics. To visualize this we present below several visual results of Example-based Super-Resolution, once using internal examples, and once using external examples (from a database of 200 images). In Sec. 4 (and above) the empirical evaluations were computed for x2 Super-Resolution factors. However, for visualization purposes, we show x3 Super-Resolution factors, because the hallucination and blur effects become more pronounced and easier to see visually as the prediction gap grows.